How to find pattern in the following polynomials with mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg104108] How to find pattern in the following polynomials with mathematica*From*: barefoot gigantor <barefoot1980 at gmail.com>*Date*: Mon, 19 Oct 2009 07:13:38 -0400 (EDT)

1: 1+ (6n + 5)/(12n^2 + 12n + 1) 2: 1+ (150n^2 + 200n + 55)/(300 n^3 + 450 n^2 + 160 n + 5) 3: 1+ (420 n^3+770 n^2+410 n+57) / (840 n^4+1680 n^3+1030 n^2+190 n+3) 4: 1+ (630 n^4+1470 n^3+1155 n^2+343 n+29)/(1260 n^5+3150 n^4+2730 n^3+945 n^2+107 n+1) 5: 1 + (13860 n^5+39270 n^4 + 40740 n^3+18711 n^2+3591 n+205)/(27720 n^6+83160 n^5+93030 n^4+47460 n^3+10689 n^2+819 n+5)